Question

What is the area of the shaded portion of the circle?

Answer 1

Answer:

1st option

Step-by-step explanation:

the area of the shaded portion is calculated as

area of sector - area of white Δ

area of sector = area of circle × fraction of circle

                        = πr² × $\frac{90}{360}$ ( r is the radius )

                        = π × 8² × $\frac{1}{4}$

                       = 64π × $\frac{1}{4}$

                       = 16π in²

area of Δ = $\frac{1}{2}$ bh ( b is the base and h the perpendicular height )

here b = h = 8

area of Δ = $\frac{1}{2}$ × 8 × 8 = $\frac{1}{2}$ × 64 = 32 in²

then

area of shaded portion = (16π - 32 ) in²